This invention relates to the reduction of quantization noise in digital signals produced by oversampling an analog signal.
In numerous fields of application, e.g., sound recording and reproduction, seismic exploration, medical imaging, and scientific data acquisition, it is often desirable to represent analog signals by digital approximations to sampled values taken at regular time intervals; this may be for the sake of convenience of processing or of storage, for example. In the favorable case where the signal is bandlimited, it is known from the Shannon theorem that no information is lost due to sampling when a signal is sampled at a rate more than twice the frequency of its highest-frequency component (Nyquist sampling rate.) On the other hand, quantizing the samples inevitably results in distortion., The quantized signal may then be regarded as the sum of the original signal and a "quantization noise."
In its simplest form, an analog-to-digital converter may involve sampling a signal without regard to previously obtained samples. Of interest also is the addition of a "dither signal" before sampling, all whose component frequencies lie outside the signal band. Alternatively, in the interest of reduced quantization noise, more sophisticated converters may use feedback as in so-called .SIGMA..DELTA.-converters.
The following represents a selection from the literature concerned with quantization noise:
U.S. Pat. No. 4,222,110, issued Sep. 9, 1980 to N. H. K. Judell discloses coupling of an integrating analog-to-digital converter to a digital filter to achieve a reduction in digitization noise and aliasing.
J. C. Candy, "Decimation for Sigma Delta Modulation", IEEE Transactions on Communications, Vol COM-34 (1986), pp. 72-76 discloses transformation of a digital representation of an oversampled analog signal, taking short words at a high sampling rate and producing longer words at a lower rate. In the process, signal-to-noise ratio remains essentially unchanged.
U.S. Pat. No. 4,754,260, issued Jun. 28, 1988 to R. G. Nelson et al. discloses an analog-to-digital converter which includes a low-pass filter for phase differences between a reference signal and a signal modulated by an analog signal of interest. The resulting signal, taken as representative of phase error in a frequency band of interest, is used to produce a corrective feedback signal.
U. Heute, "Improving A/D Conversion by Digital Signal Processing--Novel Solutions to Known Problems and New Problems," Frequenz, Vol. 42 (1988), pp. 93-101 discloses oversampling analog-to-digital converters in which a linear predictor scheme is used to predict a signal sample from a linear combination of a number of preceding samples.
T. Cataltepe et al., "Digitally Corrected multi-bit .SIGMA..DELTA. Data Converters", Proceedings, IEEE International Symposium on Circuits and Systems, Vol. 1 (1989), pp. 647-650 discloses analog-to-digital converters in which digital correction schemes are used to compensate for nonlinearities in the digital-to-analog conversion of a feedback signal.
F. Harris et al., "New Results with Oversampled Converters", Conference Record, Twenty-Third Annual Asilomar Conference on Signalling Systems and Computers, Asilomar Conference on Circuits, Systems, and Computers, Vol. 2, Maple Press, 1989, pp. 844-848 discloses a two-step analog-to-digital converter in which, before digitization, an analog input signal is first converted to an analog quantized form.
In classical Nyquist-rate analog-to-digital conversion, the power of quantization noise is quadratically related to the quantizing interval and, if the quantizing subdivision is fine enough, the noise signal has a uniform distribution of amplitude ("white noise") in the signal band. In the case of oversampling, i.e., sampling a bandlimited signal at a rate higher than the Nyquist rate, the noise power spectrum can spread out of the signal band, so that oversampling can result in reduced noise in the signal band. In simple analog-to-digital conversion, if the quantization error signal is uncorrelated with the input signal, the error-signal power (or mean-square error, MSE) is reduced by a factor equal to the oversampling rate, R=f.sub.s /2f.sub.m. If the quantizer is an n-th order single-path .SIGMA..DELTA.-converter, the reduction is proportional to R.sup.2n+1. The present invention is motivated by the desire to further reduce quantization noise in analog-to-digital conversion methods involving oversampling.